OP, I think the bigger issue is that your spouse doesn't feel like he/she can be open with you, for whatever reason. It could be his/her fault, or it could be yours--obviously I can't say because I don't know either of you. I suggest you ask that you both see a counselor. I have a friend who is a pastor, and he sees a counselor with his wife once a year... he likens it to keeping up maintenance on your car: just check it out, make sure things are running smoothly. It can't hurt.

Occasional Googling is one thing. Curiosity is a real thing. But weekly Googling the same person??? I think that wold clearly be an indication that things might be wrong. I started Googling an Ex a few years ago, and we started chatting and communicating via facebook. Either he realized this was a problem or his wife did, but it pretty much ended and I haven't heard from him again. Until I read your post I didn't put two and two together that I was doing this at the Googling and reaching out to him at beginning of the end of my marriage. It was me looking elsewhere for some love and validation and attraction that I was not feeling at home. Instead of looking at myself and my husband and my marriage to figure out what was wrong, I was groping around for external validation, love, attention, whatever. Because there were things wrong (I can see it very clearly now) and I was avoiding the real issues.

I google exes occasionally because I've completely lost touch and I'm curious about what might have become of them. I wouldn't be interested in dating them again, but once someone has been in my life, I might wonder down the road where they ended up. I've also googled old friends, teachers, etc.

I'd probably be a bit taken aback if my husband continued to google the same person. Is this person doing something extremely interesting for a living or a hobby that he might be keeping up with? Like if I had an ex who was doing ironman triathlons, I might see what their last race time was, or something.